Colóquio de Matemática

Optimal transport, heat, and entropy

Sala 6.2.33, Ciências ULisboa (com transmissão via Zoom)

Por Léonard Monsaingeon (Ciências ULisboa - GFM).

Optimal transport consists in displacing "mass" (e.g. a pile of sand) from a source location to a target destination, while minimizing the amount of energy spent along the process. The original formulation, due to G. Monge in 1781, is highly nonlinear. However, L. Kantorovich managed in the 1950's to recast the problem in a linear form, which allowed in the last 20 years to completely revisit the theory and unveil unsuspected connections with other branches of mathematics. In this talk I will take interested in the heat equation $\partial_t u=\Delta u$, which is the most basic parabolic PDE. Using optimal transport I will show how this linear evolution equation can be "non-linearized" in order to recover somehow a strong second principle of thermodynamics: not only entropy increases over time, but in in a certain sense the heat equation actually makes this loss of information as fast as possible.

Transmissão via Zoom (Meeting ID: 675 181 2409).

16h00
Departamento de Matemática | Ciências ULisboa

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